OPEN PROBLEMS IN THE THEORY OF NON-UNIFORM HYPERBOLICITY

被引：16
|
作者：
Pesin, Yakov [1 ]
Climenhaga, Vaughn [1 ]
机构：
[1] Penn State Univ, Dept Math, University Pk, PA 16802 USA
来源：
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS | 2010年 / 27卷 / 02期
基金：
美国国家科学基金会;
关键词：
Non-uniform hyperbolicity; generic properties; mixed hyperbolicity; conservative systems; dissipative systems; SRB measures; u-measures; LYAPUNOV EXPONENTS; STABLE ERGODICITY; INVARIANT TORI; ATTRACTORS; EXISTENCE; DYNAMICS; SYSTEMS; GENERICITY; ABUNDANCE;
D O I：
10.3934/dcds.2010.27.589
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
This is a survey-type article whose goal is to review some recent developments in studying the genericity problem for non-uniformly hyperbolic dynamical systems with discrete time on compact smooth manifolds. We discuss both cases of systems which are conservative (preserve the Riemannian volume) and dissipative (possess hyperbolic attractors). We also consider the problem of coexistence of hyperbolic and regular behaviour.
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页码：589 / 607
页数：19
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